Journal of Mathematical Sciences, Vol. 138, No. 4, 2006 LOCAL THEORY OF SETS AS A FOUNDATION FOR CATEGORY THEORY AND ITS CONNECTION WITH THE ZERMELOнFRAENKEL SET THEORY V. K. Zakharov, E. I. Bunina, A. V. Mikhalev, and P. V. Andreev UDC 510.223, 512.581 CONTENTS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. First-Order Theories and LTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1. Language of first-order theories .

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